This paper deals with the problem of scheduling feeding tasks of a single mobile robot which has capability of supplying parts to feeders on production lines. The performance criterion is to minimize the total traveling time of the robot and the total tardiness of the feeding tasks being scheduled, simultaneously. In operation, the feeders have to be replenished a number of times so as to maintain the manufacture of products during a planning horizon. A method based on predefined characteristics of the feeders is presented to generate dynamic time windows of the feeding tasks which are dependent on starting times of previous replenishment. A heuristic based on genetic algorithm which could be used to produce schedules in online production mode is proposed to quickly obtain efficient solutions. Several numerical examples are conducted to demonstrate results of the proposed approach.